My first post here, I hope it's a useful one -- I went the same route after listening to my HD650s single-ended for the last 3-4 years. I picked up one of Tyll's last Balanced Home amps before the holidays and ended up returning it since I didn't need the dac either (I opted for the HR dac, and then ended up buying imho a much nicer-sounding dac, a DCC2). My current amp is a balanced beta22.
I agree with Dreadhead that the benefits of going balanced are hard to discern (esp. in light of the cost required to create a fully balanced chain from source onward); when I connected my balanced HD650s to the headroom amp, the sound was good: impactful, generally tighter bass notes, and the spacing between things improved. The nice thing about the HR balanced home was that I could A/B single ended vs. balanced from the same source just by flipping a switch. I compared a single-ended HD650/Zu Mobius against a balanced HD650/Silver Dragon and the differences were very very hard to pick out.
How different? IMHO you would probably get more benefit from finding better recorded versions of the music you like -- which are far cheaper to obtain -- than balancing your entire chain. For certain recordings I own, the balanced HD650 was amazing. However, I attribute that, in part, to the possibility that gear with balanced outputs is well-made to begin with. In addition, there is some sonic benefit to balancing the HD650s, in terms of clarity and soundstage. In my opinion, is it worth the cost of balancing? Not if the rest of your chain is lacking - in particular, your source could be limiting your soundstage in ways that a balanced headphone can't entirely correct. Plus my beta22 has a separate volume control for L/R so I increase the soundstage by slightly decreasing one channel (yeah, that's how I roll). My justification for going balanced, and staying balanced, is flexibility: you can have the best of both worlds since balanced gear can also be used single-ended. I realize that curiosity may be gnawing at you (like it did me), and I haven't really answered your original question so here goes:
With regards to choosing a balanced ss amp, I think the HD650 requires a good amp regardless of drive (balanced or single-ended) since it scales to better sources and amps. The better the amp, the better the sound - 'better' being subjective of course. You can safely assume that the balanced variations of good SS single-ended choices apply here (Gilmore Lite comes to mind, and I own a PPA that seems to demolish things every time I go back to it). That said, I don't think a balanced Mini3 will get you somewhere a single-ended Mini3 could not.
I listened to four balanced source outputs with balanced HD650s, two were dedicated amps (a HR balanced home and a beta22), and two were the attenuated balanced outs of dacs (a benchmark dac1 and a dcc2). Here is my subjective ranking:
Beta22 > DCC2 outputs > HR balanced home (max module) > DAC1
I haven't heard the single-ended versions of all these but here is an attempt to characterize the single ended flavors that I've heard: PPA > Gilmore Lite (w/the PSU) I know, blasphemy > DAC1 headphone amp.
So for both balanced and single-ended, the DIY designs top out, and the DAC1 comes up in the end spot. Notice that -- to my ears -- the single-ended vs. balanced ranking does not affect the quality of the amps in relation to one another -- they are positionally the same regardless of whether I was listening balanced or single-ended. If I had to make amp choices again, I would base my balanced decision on how the single-ended SS sibling (if there is one) drives the single-ended HD650.
Of course, my SS impressions could change when my EC Balancing Act arrives in a month or so.
.
.